Introduction to Probability

Probability of an Event

Probabilities are associated with experiments where the outcome is not known in advance or cannot be predicted. For example, if you toss a coin, will you obtain a head or tail? If you roll a die will obtain 1, 2, 3, 4, 5 or 6?
Probability measures and quantifies "how likely" an event, related to these types of experiment, will happen. The value of a probability is a number between 0 and 1 inclusive. An event that cannot occur has a probability (of happening) equal to 0 and the probability of an event that is certain to occur has a probability equal to 1.(see probability scale below).

In order to quantify probabilities, we need to define the sample space of an experiment and the events that may be associated with that experiment.

Example 7: A die is rolled, find the probability of getting a 3.
The event of interest is "getting a 3". so E = {3}.
The sample space S is given by S = {1,2,3,4,5,6}.
The number of possible outcomes in E is 1 and the number of possible outcomes in S is 6. Hence the probability of getting a 3 is
P(E) = 1 / 6.
Example 8: A die is rolled, find the probability of getting an even number.
The event of interest is "getting an even number". so E = {2,4,6}, the even numbers on a die.
The sample space S is given by S = {1,2,3,4,5,6}.
The number of possible outcomes in E is 3 and the number of possible outcomes in S is 6. Hence the probability of getting an even number is
P(E) = 3 / 6 = 1 / 2.